where \(\mathbf {r}_u = (r_{u1}, \dots , r_{un})\)  is the \(u\) -th user vector of \(\mathbf {R}\) , \(\lambda \)  is the regularization coefficient, and \(\Omega (\cdot )\)  is a regularization function. Conventional AE-based models [1]}, [2]} have been widely used the cross-entropy loss function \(\mathcal {L}_{CE}\)  as the surrogate function for the top-N recommendation problem:
\(\mathcal {L}_{CE}(\mathbf {r}_u, \mathbf {\hat{r}}_u) = - \sum _{i=1}^{n}{r_{ui}\log \hat{r}_{ui} + (1 - r_{ui})\log (1 - \hat{r}_{ui})},\) 
